Samantha had 25% more pencils than Andrew. Isabella had 50% fewer pencils than Samantha. Samantha and Andrew gave Isabella some pencils in the ratio of 1 : 5. As a result, Isabella had 60% more pencils than before. Given that Andrew had 45 less pencils than Isabella in the end, how many pencils did Andrew give to Isabella?

Samantha	Andrew	Isabella
5x2	4x2
2x5		1x5
10	8	5

100% + 25% = 125%
125% = ¹²⁵₁₀₀ = ⁵₄

Samantha : Andrew = 5 : 4

100% - 50% = 50%
50% = ⁵⁰₁₀₀ = ¹₂

Samantha : Isabella = 2 : 1

The number of pencils that Samantha had at first is repeated. Make the number of pencils that Samantha had at first the same.  LCM of 5 and 2 is 10.

	Samantha	Andrew	Isabella
Before	10x2 =  20 u	8x2 = 16 u	5x2 = 10 u
Change			+ 3x2 = + 6 u
Comparing the changes in the number of pencils	- 1x1 = - 1 u	- 5x1 = - 5 u	+ 6x1 = + 6 u
After	19 u	11 u	8x2 = 16 u

60% x 5 
= ⁶⁰₁₀₀ x 5 
= 3 

The total number of pencils that Samantha and Andrew gave to Isabella is repeated.  Make the total number of pencils that Samantha and Andrew gave to Isabella the same.  LCM of 6 and 3 is 6.

Number of pencils that Andrew had less than Isabella 
= 16 u - 11 u
= 5 u

5 u = 45

1 u = 45 ÷ 5 = 9

Number of pencils that Andrew gave to Isabella
= 5 u
= 5 x 9
= 45

Answer(s): 45